Not that I am aware of. Anything beyond 2 decimal places will be shifted by N decimal places x 10 or in other by example: you post a price of 3.12345 but it will be saved as 312345.00.
Generally speaking, rounding at the actaul monetary limit is good for most commerce applications. You cannot cut a 1 cent coin in to two so why would you in this case. Of course, that assumption comes with one big boat load full of its own issues. Some currencies actually have more than 2 decimal places. Who carries the rounding cost - does the merchant pay the difference or the customer? Accounting ledgers can often be maintained with high precision i.e. every fraction is accounted for, but then all of a sudden your accounting ledger and store's ledger won't match - how do you account for that? And of course, you may be dealing with micro transactions - in this case, I don't believe Shopify is a suitable platform and doubt any of the generic ecommerce platforms would be.
Hope this helps!
I think we misunderstood each other. While you can post more than 2 decimal points in monetary values, the API, Admin and Storefront do not work with those values because
1.2345 becomes 12345.00
So your product you assume costs $1.2345 will now cost $12,345.00. Best check for yourself to see what I mean.